Applying MCDEA Models to Rank Decision Making Units with Stochastic ‎Data

Subject Areas : International Journal of Industrial Mathematics

علی غفران ¹ , مسعود صانعی ² , قاسم توحیدی ³ , حسین بورانی ⁴

1 - Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran
2 - Department of Mathematics, Islamic Azad University, Tehran-Center Branch, Tehran, Iran
3 - Department of Mathematics, Islamic Azad University, tehran-Center Branch, Tehran, Iran.
4 - Departments of Statistics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran

Received: 2019-04-28 Accepted : 2021-01-18 Published : 2021-04-01

Keywords: Data envelopment analysis (DEA), Stochastic Data, Ranking, ‎Probability‎, Multiple criteria DEA (MCDEA),

Abstract :

As a technique based on mathematical programming, Data Envelopment Analysis (DEA) is used for evaluating the efficiency of homogeneous Decision Making Units (DMUs). DEA models need accurate input and output data. In many situations, on the one hand, accurate measurement of inputs and outputs is difficult due to their volatility and complexity. This conflict results in uncertain DEA models. Its main problem is transformation of deterministic equivalent of stochastic model into quadratic programming, time-consuming and complexity and it requires presuppositions. By means of Bi-objective multiple criteria DEA (Bio-MCDEA) model that considers stochastic data, our proposed model reduces some of these problems and facilitates problem solving through presenting primary presupposition and final linear model. The efficiency score of DMUs is determined by applying stochastic Bio- MCDEA model. Eventually, we used the data of seventeen Iranian electricity distribution companies to illustrate the methods developed in the present paper.

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